Related provisions for IFPRU 6.1.12
1 - 20 of 28 items.
A VaR model permission will generally set out the broad classes of position within each risk category in its scope. It may also specify how individual products within one of those broad classes may be brought into or taken out of scope of the VaR model permission. These broad classes of permission are as follows:(1) linear products, which comprise securities with linear pay-offs (such as bonds and equities) and derivative products which have linear pay-offs in the underlying risk
A firm should ensure that the data series used by its VaR model is reliable. Where a reliable data series is not available, proxies or any other reasonable value-at-risk measurement may be used when the firm demonstrates that the requirements of article 367(2)(e) of the UK CRR1 (Requirements for risk measurement) are met. A firm should demonstrate that the technique is appropriate and does not materially understate the modelled risks
A firm is expected to update data sets to ensure standards of reliability are maintained in accordance with the frequency set out in its VaR model permission, or more frequently if volatility in market prices or rates necessitates more frequent updating. This is in order to ensure a prudent calculation of the VaR measure.
(1) In determining whether it is appropriate for a firm to use empirical correlations within risk categories and across risk categories within a model, the FCA expects certain features to be observed in assessing whether such an approach is sound and implemented with integrity. In general, the FCA expects a firm to determine the aggregate VaR measure by adding the relevant VaR measure for each category, unless the firm's permission provides for a different method of aggregating
If the day on which a loss is made is day n, the value-at-risk measure for that day will be calculated on day n-1, or overnight between day n-1 and day n. Profit and loss figures are produced on day n+1, and back-testing also takes place on day n+1. The firm's supervisor should be notified of any overshootings by close of business on day n+2.
Any overshooting initially counts for the purpose of the calculation of the plus factor, even if subsequently the FCA agrees to exclude it. Thus, where the firm experiences an overshooting and already has four or more overshootings for the previous 250 business days, changes to the multiplication factor arising from changes to the plus factor become effective at day n+3.
The FCA, will review as part of a firm's VaR model permission application, the processes and documentation relating to the derivation of profit and loss used for back-testing. A firm's documentation should clearly set out the basis for cleaning profit and loss. To the extent that certain profit and loss elements are not updated every day (for example, certain reserve calculations) the documentation should clearly set out how such elements are included in the profit and loss s
In accordance with article 363(3) of the UK CRR1 (Permission to use internal models), the FCA expects a firm to provide and discuss with us details of any significant planned changes to the VaR model before those changes are implemented. These details must include detailed information about the nature of the change, including an estimate of the impact on VaR numbers and the incremental risk charge.
The use of overlapping intervals of 10-day holding periods for article 365 of the UK CRR1 (VaR and stressed VaR calculation) introduces an autocorrelation into the data that would not exist should truly independent 10-day periods be used. This may give rise to an under-estimation of the volatility and the VaR at the 99% confidence level. To obtain clarity on the materiality of the bias, a firm should measure the bias arising from the use of overlapping intervals for 10-day VaR
Article 365 of the UK CRR1 requires a firm that uses an internal model for calculating its own funds requirement to calculate, at least weekly, a stressed VaR (sVaR) of their current portfolio. When the FCA considers a firm's application to use a sVaR internal model it would expect the features in IFPRU 6.3.20 G to IFPRU 6.3.24 G to be present prior to permission being granted, as indicative that the conditions for granting permission have been met.
The firm should calculate the sVaR measure to be greater than or equal to the average of the 2nd and 3rd worst loss in a 12-month time series comprising of 250 observations. The FCA expects, as a minimum, that a corresponding linear weighting scheme should be applied if the firm uses a larger number of observations.
The firm should ensure that the sVaR period chosen is equivalent to the period that would maximise VaR, given the firm's portfolio. There is an expectation that a stressed period should be identified at each legal entity level at which capital is reported. Therefore, group level sVaR measures should be based on a period that maximises the group level VaR, whereas entity level sVaR should be based on a period that maximises VaR for that entity.
The following information is expected to be submitted quarterly:(1) analysis to support the equivalence of the firm's current approach to a VaR-maximising approach on an ongoing basis; (2) the rationale behind the selection of key major risk factors used to find the period of significant financial stress;(3) summary of ongoing internal monitoring of stressed period selection with respect to current portfolio; (4) analysis to support capital equivalence of upscaled 1-day VaR and
Article 372 of the UK CRR1 (Requirement to have an internal IRC model) requires a firm that use an internal model for calculating own funds requirements for specific risk of traded debt instruments to also have an internal incremental default and migration risk (IRC) model in place to capture the default and migration risk of its trading book positions that are incremental to the risks captured by its VaR model. When the FCA considers a firm's application to use an IRC internal
The FCA expects the IRC model to capitalise pre-default basis risk. In this respect, the model should reflect that in periods of stress the basis could widen substantially. The firm should disclose to the FCA its material basis risks that are incremental to those already captured in existing market risk capital measures (VaR-based and others). This must take actual close-out periods during periods of illiquidity into account.
To achieve a soundness standard comparable to those under the IRB approach, LGD estimates should reflect the economic cycle. Therefore, the FCA expects a firm to incorporate dependence of the recovery rate on the economic cycle into the IRC model. Should the firm use a conservative parameterisation to comply with the IRB standard of the use of downturn estimates, evidence of this should be submitted in quarterly reporting to the FCA, bearing in mind that for trading portfolios,
The FCA expects that an IPRE rating system will only be compliant if a firm is able to demonstrate the following in respect of its treatment of cash flows (except where the firm can demonstrate that this is not an appropriate risk driver):(1) the difference in deal ratings when tenant ratings are altered is intuitive;(2) the transformation of ratings into non-rent payment probability is intuitive. Even where tenants are rated by the firm the PD will not usually represent a direct
The FCA expects that firms will not be compliant with the calibration requirements relating to use of a long-run default rate, unless it can demonstrate that:(1) the internal data series is the longest relevant and accurate data series, on a UK CRR2 compliant definition of default, that is available;(2) the determination of long-run default rate includes reference to an appropriate source of downturn data (this may require the use of external data);(3) the relevance of any external
The FCA expects that a firm will only be compliant with the calibration requirements relating to model philosophy if it can demonstrate that:(1) the model philosophy is clearly articulated and justified. Justification should include analysis of the performance of assets, and the corresponding ratings assigned, over a change in economic conditions (ie, as long as period as possible); and(2) in addition to encapsulating this information in a coherent way in the calibration, the
Where the rating system is classed as a low default portfolio in accordance with the guidance in this section, a firm should be able to demonstrate that the framework applied adequately considers:(1) economic environment of data used;(2) changes in portfolio composition over time;(3) parameter choices; and(4) model philosophy.
Under article 144(1) of the UK CRR2, all models, including those constructed from a theoretical basis without reference to any empirical default data (such as Monte-Carlo cash-flow simulation models), must meet the IRB requirements that are set out in Title II Chapter 3 of Part Three of the UK CRR2 (IRB approach).
The FCA considers that, to meet the requirements referred to in IFPRU 4.11.1 G, it will be necessary for firms to demonstrate that a firm has a good understanding of PD models that are constructed theoretically and that the parameter estimates reflect a one-year PD. In addition, even if empirical data were not used to determine the PD estimate it should, where available, be used to back-test the estimates.
The FCA expects that, as most models of this type will be able to produce one-year estimates of PD that correspond closely to point-in-time estimates, firms should conduct robust back-testing of such estimates by comparing them with realised default rates. Firms would need to demonstrate that the results of such back-testing meet pre-defined and stringent standards in order for the FCA to be satisfied that the IRB requirements are met.
Because assumptions in the model build process are likely to materially impact the resulting PDs, the FCA would expect these choices to be clearly justified in the model documentation and to have been independently reviewed. To be satisfied that a firm is complying with article 176(1)(d) of the UK CRR2, the FCA expects a firm to support justification for all assumptions with analysis of the sensitivity of the model outputs to changes in the assumptions.
The FCA expects that a firm will be compliant with the validation requirements only where1it can demonstrate, in respect of discriminatory power, that:11(1) appropriate minimum standards that the rating system is expected to reach are defined, together with reasoning behind the adoption of such standards and that the factors considered when determining the tests are clearly documented;(2) an objective rank-ordering metric, measured using an appropriate time horizon (eg, using
The FCA expects that a firm will be compliant with the validation requirements only where1it can demonstrate in respect of the calibration that:11(1) observed default rate versus PD is considered at grade level and across a range of economic environments (ie, as long as period as possible);(2) where the PD does not relate to a pure point-in-time estimate, either the PD or the observed default rate is transformed such that comparison between the two is meaningful. This transformation
(1) The methodology for the identification of the risks in IFPRU 6.1.4 R and the calculation of those additional own funds for value-at-risk (VaR) and stressed value-at-risk (stressed VaR) models is called the "RNIV framework". A firm is responsible for identifying these additional risks and this should be an opportunity for risk managers and management to better understand the shortcomings of the firm's models. Following this initial assessment, the FCA will engage with the firm
The pricing model used to calculate delta should be:(1) based on appropriate assumptions which have been assessed and challenged by suitably qualified parties independent of the development process; (2) independently tested, including validation of the mathematics, assumptions, and software implementation; and(3) developed or approved independently of the trading desk.
A firm should have adequate systems and controls in place when using pricing models to calculate deltas. This should include the following documented policies and procedures:(1) clearly defined responsibilities of the various areas involved in the calculation;(2) frequency of independent testing of the accuracy of the model used to calculate delta; and(3) guidelines for the use of unobservable inputs, where relevant.
A significant IFPRU firm should consider developing internal specific risk assessment capacity and to increase use of internal models for calculating own funds requirements for specific risk of debt instruments in the trading book, together with internal models to calculate own funds requirements for default and migration risk where its exposures to specific risk are material in absolute terms and where it holds a large number of material positions in debt instruments of different
The FCA expects that, over time, the actual default rates incurred in each segment would form the basis of PD estimates for the segments. However, at the outset, the key calibration issue is likely to be the setting of the initial long-run default rate for each segment, as this will underpin the PD of the entire portfolio for some years to come. A firm should apply conservatism in this area and this is something on which the FCA is likely to focus on in model reviews.
To ensure that a rating system provides a meaningful differentiation of risk and accurate and consistent quantitative estimates of risk, the FCA expects a firm to develop country-specific mid-market PD models. Where a firm develops multi-country mid-market PD models, the FCA expects the firm to be able to demonstrate that the model rank orders risk and predicts default rates for each country where it is to be used for own funds requirements calculation.
The FCA expects a firm to estimate PD for a rating system in line with this section where the firm's internal experience of defaults for that rating system was 20 defaults or fewer, and reliable estimates of PD cannot be derived from external sources of default data, including the use of market price-related data. In PD estimation for all exposures covered by the rating system, the FCA expects the firm to:(1) use a statistical technique to derive the distribution of defaults implied
The areas of responsibility for the credit risk control unit(s) must include the following:(1) testing and monitoring grades and pools;(2) production and analysis of summary reports from the firm'srating systems;(3) implementing procedures to verify that grade and pool definitions are consistently applied across departments and geographic areas;(4) reviewing and documenting any changes to the rating process, including the reasons for the changes;(5) reviewing the rating criteria
Notwithstanding BIPRU 4.3.16 R, a firm using pooled data according to BIPRU 4.3.92 R - BIPRU 4.3.94 R (Overall requirements for estimation) may outsource the following tasks:(1) production of information relevant to testing and monitoring grades and pools;(2) production of summary reports from the firm'srating systems;(3) production of information relevant to review of the rating criteria to evaluate if they remain predictive of risk;(4) documentation of changes to the rating
A firm must document the rationale for and analysis supporting its choice of rating criteria. A firm must document all major changes in the risk rating process, and such documentation must support identification of changes made to the risk rating process subsequent to the last review by the appropriate regulator. The organisation of rating assignment including the rating assignment process and the internal control structure must also be documented.[Note:BCD Annex VII Part 4 point
Where a firm employs statistical models in the rating process, the firm must document its methodologies. This material must:(1) provide a detailed outline of the theory, assumptions and/or mathematical and empirical basis of the assignment of estimates to grades, individual obligors, exposures, or pools, and the data source(s) used to estimate the model;(2) establish a rigorous statistical process (including out-of-time and out-of-sample performance tests) for validating the model;
(1) This paragraph applies to the use of statistical models and/or other mechanical methods to assign exposures to obligor grades, obligor pools, facility grades or facility pools.(2) A firm must be able to demonstrate to the appropriate regulator that the model has good predictive power and that capital requirements are not distorted as a result of its use.(3) The input variables to the model must form a reasonable and effective basis for the resulting predictions. The model
(1) This paragraph contains guidance on BIPRU 4.3.51 R for the use of external models.(2) BIPRU 4.3.51 R (2) - BIPRU 4.3.51 R (8) also apply to mechanical methods to assign exposures or obligors to facility grades or pools and to a combination of models and mechanical methods.(3) The standards which a firm applies to an external model should not be lower than those for internal models. (4) The appropriate regulator will not accredit any individual model or vendor. The burden is
If a firm uses a rating model to assign exposures to the borrower or facility grades, it may reflect the data on main drivers of risk parameters by its inclusion in the model as a risk driver or as part of a subsequent process that adjusts the output of that model to calculate the risk parameters PD, LGD, conversion factor and EL.
(1) If:(a) a firm's internal experience of exposures of a type covered by a model or other rating system is 20 defaults or fewer; and(b) in the firm's view, reliable estimates of PD cannot be derived from external sources of default data, including the use of market price related data, for all the exposures covered by the rating system;the firm must estimate PD for exposures covered by that rating system in accordance with this rule.(2) A firm must use a statistical technique
There are a number of general methodologies for calculating PRR using a VaR model. The appropriate regulator does not prescribe any one method of computing VaR measures. Moreover, it does not wish to discourage any firm from developing alternative risk measurement techniques. A firm should discuss the use of any alternative techniques used to calculate PRR with the appropriate regulator.
A firm may meet the requirement in BIPRU 7.10.26R by using different model parameters and employing a suitable adjustment mechanism to produce a figure which is equivalent to the figure produced using the parameters set out in BIPRU 7.10.26R. For example, a firm's model may use a 95% one-tailed confidence limit if the firm has a mechanism to convert the output of the model to reflect a 99% one-tailed confidence limit.
3A firm must validate its approach to incremental risk charge. In particular, a firm must: (1) validate that its modelling approach for correlations and price changes is appropriate for its portfolio, including the choice and weights of its systematic risk factors;(2) perform a variety of stress tests (not limited to the range of events experienced historically), including sensitivity analysis and scenario analysis, to assess the qualitative and quantitative reasonableness of
3As part of its VaR model permission, the appropriate regulator may authorise a firm to use the all price risk measure to calculate an additional capital charge in relation to positions in its correlation trading portfolio if it meets the following minimum standards:(1) it adequately captures all price risks at a 99.9% confidence interval over a capital horizon of one year under the assumption of a constant level of risk, and adjusted, where appropriate, to reflect the impact
A firm with a complex portfolio is expected to demonstrate greater sophistication in its modelling and risk management than a firm with a simple portfolio. For example, a firm will be expected to consider, where necessary, varying degrees of liquidity for different risk factors, the complexity of risk modelling across time zones, product categories and risk factors. Some trade-off is permissible between the sophistication and accuracy of the model and the conservatism of underlying
Firms who gained model recognition before 1 January 2007 will be permitted to calculate PRR for specific risk in accordance with the methodology they were permitted to use immediately before that date instead of capturing event and default risk in their models (see BIPRU TP 14 (Market risk: VaR models)). This treatment will not be available to a firm that gains model recognition after that date.
In relation to a firm whose activities are moderately complex, in carrying out its ICAAP, BIPRU 2.2.25 G (3) to (4) apply. In addition, it could:(1) having consulted the management in each major business line, prepare a comprehensive list of the major risks to which the business is exposed;(2) estimate, with the aid of historical data, where available, the range and distribution of possible losses which might arise from each of those risks and consider using shock stress tests
(1) This paragraph applies to a proportional ICAAP in the case of a firm whose activities are complex.(2) A proportional approach to that firm'sICAAP should cover the matters identified in BIPRU 2.2.26 G, but is likely also to involve the use of models, most of which will be integrated into its day-to-day management and operation.(3) Models of the sort referred to in (2) may be linked so as to generate an overall estimate of the amount of capital that a firm considers appropriate
If a firm adopts a top-down approach to developing its internal model, it should be able to allocate the outcome of the internal model to risks it has previously identified in relation to each separate legal entity, business unit or business activity, as appropriate. In relation to a firm which is a member of a group, GENPRU 1.2.53 R (Application of GENPRU 1.2 on a solo and consolidated basis: Processes and tests) sets out how internal capital identified as necessary by that firm'sICAAP
If a firm's internal model makes explicit or implicit assumptions in relation to correlations within or between risk types, or in relation to diversification benefits between business types, the firm should be able to explain to the appropriate regulator, with the support of empirical evidence, the basis of those assumptions.
The values assigned to inputs into a firm's model should be derived either stochastically, by assuming the value of an item can follow an appropriate probability distribution and by selecting appropriate values at the tail of the distribution, or deterministically, using appropriate prudent assumptions. For options or guarantees which change in value significantly in certain economic or demographic circumstances, a stochastic approach would normally be appropriate.
Where a firm adjusts assumed house price values within its LGD models to take account of current market conditions (for example, appropriate house price indices), the FCA recognises that realised falls in market values may be captured automatically. A firm adopting such approaches may remove observed house price falls from its downturn house price adjustment so as not to double count. A firm wishing to apply such an approach must seek the consent of the FCA and be able to demonstrate
The FCA uses a framework for assessing the conservatism of a firm's wholesale LGD models for which there are a low number of defaults. This framework is set out in IFPRU 4 Annex 2G (Wholesale LGD and EAD framework) and does not apply to sovereign LGD estimates which are floored at 45%. This framework is also in the process of being used to assess the calibration of a firm's material LGD-models for low-default portfolios.
In the following cases, the FCA expects a firm to determine the effect of applying the framework in IFPRU 4 Annex 2G (Wholesale LGD and EAD framework) to models which include LGD values that are based on fewer than 20 'relevant' data points (as defined in IFPRU 4 Annex 2G):(1) the model is identified for review by the FCA; or(2) the firm submits a request for approval for a material change to its LGD model.
Without prejudice to other provisions in BIPRU 7.7, a position in a CIU is subject to a collective investment undertaking PRR (general market risk and specific risk) of 32%. Without prejudice to provisions in BIPRU 7.5.18R (Foreign currency PRR for CIUs) or, if the firm has a VaR model permission, BIPRU 7.10.44R (Commodity risks and VaR models) taken together with BIPRU 7.5.18R, where the modified gold treatment set out in those rules is used, a position in a CIU is subject to
(1) Where a firm is aware of the underlying investments of the CIU on a daily basis the firm may look through to those underlying investments in order to calculate the securities PRR for position risk (general market risk and specific risk) for those positions in accordance with the methods set out in the securities PRR requirements or, if the firm has a VaR model permission, in accordance with the methods set out in BIPRU 7.10 (Use of a Value at Risk Model).(2) Under this approach,
Where BIPRU 7.7 permits a firm to calculate the PRR charge for a position in a CIU using the rules in BIPRU 7 relating to the underlying investment, a firm that has:(1) a CAD 1 model waiver that covers positions in CIUs may use the rules as modified by that waiver; and(2) a VaR model permission that covers positions in CIUs may use its VaR model.
A firm is required under GENPRU 2.1.52 R (Calculation of the market risk capital requirement) to calculate its market risk capital requirement using the rules in BIPRU 7. However, the appropriate regulator may at the firm's request modify GENPRU 2.1.52 R to allow the firm to calculate all or part of the PRR for the positions covered by that model by using a CAD 1 model (for options risk aggregation and/or interest rate pre-processing) or a VaR model (value at risk model) instead.
Waivers permitting the use of models in the calculation of PRR will not be granted if that would be contrary to BIPRU. When granting any ‘waivers’ the FCA will have regard to the CAD.1 Accordingly, the only waivers permitting the use of models in calculating PRR that the appropriate regulator is likely to grant are CAD 1 model waivers and VaR model permissions.
The appropriate regulator does not specify the methodology that a firm should employ in order to produce the appropriate outputs from its options risk aggregation CAD 1 model. However, BIPRU 7.9.27G - BIPRU 7.9.43G provide details of how a firm could meet the requirement to capture gamma, vega and rho risks using a scenario matrix approach. Where a firm adopts the scenario matrix approach then the standards set out in BIPRU 7.9.27G - BIPRU 7.9.43G should be followed. The firm
Subject to any IRB permission of the type described in BIPRU 9.12.28 G, in the case of an originator or sponsor unable to calculate KIRB and which has not obtained approval to use the ABCP internal assessment approach, and in the case of other firms where they have not obtained approval to use the supervisory formula method or, for positions in ABCP programmes, the ABCP internal assessment approach, a risk weight of 1250% must be assigned to securitisation positions which are
Article 331(2) of the UK CRR1 (Interest rate risk in derivative instruments) states conditions that must be met before a firm not using interest rate pre-processing models can fully offset interest-rate risk on derivative instruments. One of the conditions is that the reference rate (for floating-rate positions) or coupon (for fixed-rate positions) should be 'closely matched'. The FCA will normally consider a difference of less than 15 basis points as indicative of the reference
(1) The FCA's starting assumption is that all overshootings should be taken into account for the purpose of the calculation of addends. If a firm believes that an overshooting should not count for that purpose, then it should seek a variation of its VaR model permission under article 363 of the UK CRR1 (Permission to use internal models) in order to exclude that particular overshooting. The FCA would then decide whether to agree to such a variation. (2) One example of when a firm's
The risk weighted exposure amount is the potential loss on the firm'sequity exposures as derived using internal value-at-risk models subject to the 99th percentile, one-tailed confidence interval of the difference between quarterly returns and an appropriate risk-free rate computed over a long-term sample period, multiplied by 12.5. The risk weighted exposure amounts at the equity exposure portfolio2 level must not be less than the total of the sums2 of the minimum risk weighted
(1) A firm must meet the standards set out in (2) to (9) for the purpose of calculating capital requirements.(2) The estimate of potential loss must be robust to adverse market movements relevant to the long-term risk profile of the firm's specific holdings. The data used to represent return distributions must reflect the longest sample period for which data is available and be meaningful in representing the risk profile of the firm's specific equity exposures. The data used must
(1) With regard to the development and use of internal models for capital requirement purposes, a firm must establish policies, procedures, and controls to ensure the integrity of the model and modelling process. These policies, procedures, and controls must include the ones set out in the rest of this paragraph.(2) There must be full integration of the internal model into the overall management information systems of the firm and in the management of the non-trading bookequity
(1) A firm may apply for 7a waiver in respect of:(a) the IRB approach;(b) [deleted]55(c) the CCR internal model method; and(d) the VaR model approach.(2) A firm should apply for a waiver if it wants to:(a) apply the CAD 1 model approach; or2(b) apply the master netting agreement internal models approach; or2(c) disapply consolidated supervision under BIPRU 8 for its UK consolidation group or non-UK sub-group7; or2(d) apply the treatment in BIPRU 2.1 (Solo-consolidation waiver);
(1) A firm must be able to satisfy the appropriate regulator that the firm's risk management system for managing the risks arising on the transactions covered by the master netting agreement is conceptually sound and implemented with integrity and that, in particular, the minimum qualitative standards in (2) – (11) are met.(2) The internal risk-measurement model used for calculation of potential price volatility for the transactions is closely integrated into the daily risk-management
Where there is considerable variation in the cost of the option depending on conditions at the time the option is exercised, and where that variation constitutes a material risk for the firm, it will generally be appropriate to use stochastic modelling. In this case prices from the asset model used in the stochastic approach should be benchmarked to relevant market asset prices before determining the value of the option. Where stochastic modelling is not undertaken, market option
Where the option offers a choice between two non-discretionary financial benefits (such as between a guaranteed cash sum or a guaranteed annuity value, or between a unit value and a maturity guarantee) and where there is a wide range of possible outcomes, the firm should normally model such liabilities stochastically. In carrying out such modelling firms should take into account the likely choices to be made by policyholders in each scenario. Firms should make and retain a record
If a firm uses scorecards for its internal credit approval process and the models it uses for the purpose of the IRB approach are fundamentally different from those scorecards, a firm's demonstration of how this is compatible with BIPRU 4.2.2 R (2) might include demonstrating that estimates calculated under the IRB approach are used to change sanctioning decisions at an individual or portfolio level. Examples of this might include amending cut-offs, the application of policy rules,
Where rating agency experience or the output of a statistical default model are the primary component of PD estimation, a firm should consider whether it needs to make adjustments for other relevant information, such as internal experience, conservatism and cyclical effects. In making these adjustments, a firm should consider the extent to which it needs to take account of the potential for both under-recording of actual defaults experienced and divergence of actual experience
Table: Formulae for the calculation of risk weighted exposure amounts
This table belongs to BIPRU 4.4.57 R
Correlation (R) |
0.12 × (1 - EXP(-50*PD))/(1-EXP(-50)) + 0.24* |
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[1-(1-EXP(-50*PD))/(1-EXP(-50))] |
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Maturity factor (b) |
(0.11852-0.05478*1n(PD))2 |
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(1-1.5*b)-1*(1+(M-2.5)*b)*12.5*1.06 |
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N(x) |
denotes the cumulative distribution function for a standard normal random variable (i.e. the probability that a normal random variable with mean zero and variance of one is less than or equal to x). G(z) denotes the inverse cumulative distribution function for a standard normal random variable (i.e. the value x such that N(x) = z). |
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PD = 0 |
For PD = 0, RW shall be: 0 |
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PD = 1 |
For PD = 1: |
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(i) |
for defaultedexposures where a firm applies the LGD values set out in BIPRU 4.4.32R and BIPRU 4.8.25R RW shall be: 0; |
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(ii) |
for defaultedexposures where a firm uses its own estimates of LGDs, RW shall be: Max {0, 12.5 *(LGD-ELBE)}; |
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where ELBEmust be the firm's best estimate of expected loss for the defaultedexposure according to BIPRU 4.3.122 R. |
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[Note:BCD Annex VII Part 1 point 3]
A firm should not expect the appropriate regulator to accept as adequate any particular model that the firm develops or that the results from the model are automatically reflected in any individual capital guidance given to the firm for the purpose of determining adequate capital resources. However, the appropriate regulator will take into account the results of any sound and prudent model when giving individual capital guidance or considering applications for a waiver under sections